Coin on a turntable

If I put a coin on a turntable at some distance away from the center and start turning the turntable eventually there will be a speed where the coin will fly off from the turntable.

If we put this in to calculation. We will equate the centripetal force and static friction to find out the point where the coin will fly off.

Now my question is this. The centripetal force points to the center and the static friction points the opposite direction. If centripetal force overcomes the friction, it seems to suggest the force will point towards the center instead of radially outward. But by common sense we know that the coin will fly off instead of going to the center when the revolution speed is high enough. Can someone explain why the coin fly off instead of going to the center of the turntable?

If I put a coin on a turntable at some distance away from the center and start turning the turntable eventually there will be a speed where the coin will fly off from the turntable.

If we put this in to calculation. We will equate the centripetal force and static friction to find out the point where the coin will fly off.

Now my question is this. The centripetal force points to the center and the static friction points the opposite direction.

The centripetal force is the friction force- which points toward the center. It has to overcome the "natural" motion in a straight line, tangent to the circular motion. Once that motion becomes sufficient to overcome the friction force, the coin moves "naturally", tangent to the circular motion.

If centripetal force overcomes the friction, it seems to suggest the force will point towards the center instead of radially outward. But by common sense we know that the coin will fly off instead of going to the center when the revolution speed is high enough. Can someone explain why the coin fly off instead of going to the center of the turntable?

When the friction force is not great enough to provide the centripetal force ( because speed is greater)
You should not describe the motion of the coin as " flying away from the centre"...... The coin moves in a straight line at a tangent to its circle....

The centripetal force is the friction force- which points toward the center. It has to overcome the "natural" motion in a straight line, tangent to the circular motion. Once that motion becomes sufficient to overcome the friction force, the coin moves "naturally", tangent to the circular motion.

Shouldn't the friction force always be in a direction opposite to the force applied? In this case the force is the centripetal force and the friction force should be in a direction opposite to the centripetal force?

technician - i didn't mean that the coin will fly away from the center, but just simply it will fly away.

256bits/technician/rcgldr - It is possible that the coin will return to circular path if the turntable is big enough. But once the static friction is overcome it takes less force to keep the coin moving so once the energy is depleted enough by the kinetic friction, the coin should once again return to a circular path with wider radius.

Shouldn't the friction force always be in a direction opposite to the force applied? In this case the force is the centripetal force and the friction force should be in a direction opposite to the centripetal force?

What is your point here? The centripetal force is towards the centre (which is what the term 'centripetal' means). If it is not great enough then the coin will no longer follow the same radius of circular motion. The path taken, when it slips, will be along a curve, with a radius determined by the force and the direction it acts. This curve will somewhere between a tangential line and the original circle. Actual details could be hard to work out but not impossible to do numerically, I think.
Are you confusing the reaction force on the turntable with the actual friction force on the coin?

What is your point here? The centripetal force is towards the centre (which is what the term 'centripetal' means). If it is not great enough then the coin will no longer follow the same radius of circular motion. The path taken, when it slips, will be along a curve, with a radius determined by the force and the direction it acts. This curve will somewhere between a tangential line and the original circle. Actual details could be hard to work out but not impossible to do numerically, I think.
Are you confusing the reaction force on the turntable with the actual friction force on the coin?

What I meant is shouldn't the friction force be in the opposite direction of the centripetal force (i.e pointing outward)? I thought that was the definition of friction.

There are 2 aspects to friction in this discussion.
If you picture an object on a linear conveyor belt then there is a friction force keeeping the object in contact.
With a rotating table this friction force is still present but some of the friction force now acts towards the centre....to provide the centripetal force. It means that the resultant friction force is at some angle between the radial direction and the tangential direction.
A good analogy is a car turning in a circle, the centripetal force arises from some of the friction force being 'directed' towards the centre by turning the steering wheel to turn the front wheels.
If I had to demonstrate the effect I can imagine a turntable with a ball bearing on the table. As the table rotates there is effectively no (very little) friction between the ball and the table so the table will rotate underneath the ball. I could arrange a radial, vertical arm fixed to the table so that the arm will make contact with the ball, if the vertical wall of the arm was covered in some friction material (sandpaper?) so that the force of friction between the ball and the arm was great enough to prevent sliding along the wall then the ball would rotate in circular motion on the table.
There is then only 1 effective friction force...radial and it would be the centripetal force.

I have made similar demonstrations to show some aspects of circular motion but not exactly as I have described here.....must now do it !!

PS... agree with Tanya...'centripetal' means resultant (net) force in relation to circular motion. In the same way 'restoring' means resultant in relation to SHM

What I meant is shouldn't the friction force be in the opposite direction of the centripetal force (i.e pointing outward)? I thought that was the definition of friction.

No that is not the definition of friction. Friction simply opposes relative motion that would occur in its absence. In the absence of a radially inward friction force on the puck from the turntable, the puck will acquire a non-vanishing outward radial velocity across the turntable when you turn the turntable so if you want the puck to have vanishing radial velocity across the turntable (i.e. travel in a circle) then the turntable needs to have a sufficient radially inward friction force acting on the object. This radially inward friction force is the centripetal force.

As the coin moves over the surface, friction will have two components, one which is normal to the direction of motion (providing some centipetal force to give it a curved path) and one which is in a direction opposite to its velocity.

There is clearly a radial component to the velocity of the puck if it is not traveling in a circle; it's distance from the origin is not constant in time. This is standard terminology.

As a sidenote, that leads me to address that the viewpoint of the observer or setup of the axis is important, and if not chosen correctly can lead to some bizarre intepretations.

for example:
One could argue that a rotating ball moving off tangentially when the string breaks has the same radial and tangential velocities along the path as the ball did when the string broke. Since there is no force acting on the ball to change either velocity that must be the case, and vice versu.

On the otherhand, one could also argue that since the radial distance from ball to the centre is changing, there MUST be a radial velocity. And on further analysis, as time progresses and the ball gets farther and farther away, the tangential velocity becomes zero and the ball aquires only radial velocity. The obvious conclusion here would be that there must be some unkown force acting upon the ball to change the tangential velocity into a radial velocity.

The two scenarios appear to be in contradiction. In one case there is obviously no forces acting upon the ball and in the second there obviously must be.

Well, note that both have different chosen axis. If we take the z-axis as the axis of the centre.

In the first case the x and y axis are chosen to be parallel and perpendicular to the tangent of the circle of the initial velocity of the ball when the string breaks.

In the second case, the axis are chosen to be centred upon the moving ball and ROTATING. The ROTATION of the radial axis ( the line connecting the ball and the z-axis ) and tangential axis gives rise to the ficticious force acting upon the ball.

Wasn't there some kind of problem with the motion of celestial objects years ago due to an ill-chosen, but understandable, viewpoint from an earth-center, that baffled thinkers for centuries. ( ie Copernicus and Aristotle )

PS. was technician trying to impress the same idea ( some posts are deleted and I had no chance to read them)

As the coin moves over the surface, friction will have two components, one which is normal to the direction of motion (providing some centipetal force to give it a curved path) and one which is in a direction opposite to its velocity.

That's not right, no matter how you determine velocity. In a frame rotating with the turntable, the frictional force is directed against the velocity vector, period. However, this frame also has centrifugal and coriolis accelerations that contribute to the acceleration (rotating frame).

From the perspective of an inertial frame, the frictional force is the only horizontal force present. I'll use a frame in which the center of the turntable is fixed. Once again, the frictional force is directed against the relative velocity between the coin's velocity and the point on the turntable directly underneath the coin. That point on the turntable beneath the coin will be moving faster than the coin as the coin migrates outward. Because that point is moving faster than the coin, friction with the turntable will act to speed the coin up a bit (but never to a speed as fast as that point on the turntable beneath the coin).

256: I did make some posts along those lines but they were considered to be 'irrelevant' so I deleted them rather than get involved in such discussion.
My post 14 and sophiecentres contributions are good for me.